Hence by applying [1]}, we can bound \(p\)  and \(q\)  by \(4^{N-1}\) , where \(N\)  is the number of vertices in the simple stochastic game \(G^\prime \) , as our games has out-degree 2 and uniformally random choices, as required by Condon's definitions. Thus we have \(N\le 2n(\vert V\vert \times \vert Q\vert )\)  and further we know \(\vert Q\vert  \le M^{\vert V_S\vert }\) , thus we can take \(k=2n(\vert V\vert \times \vert Q\vert )\)  and have \(1\le p,q\le 4^k\) . \(\Box \)
